A method of constructing an RF filter comprises designing an RF filter that includes a plurality of resonant elements disposed, a plurality of non-resonant elements coupling the resonant elements together to form a stop band having a plurality of transmission zeroes corresponding to respective frequencies of the resonant elements, and a sub-band between the transmission zeroes. The non-resonant elements comprise a variable non-resonant element for selectively introducing a reflection zero within the stop band to create a pass band in the sub-band. The method further comprises changing the order in which the resonant elements are disposed along the signal transmission path to create a plurality of filter solutions, computing a performance parameter for each of the filter solutions, comparing the performance parameters to each other, selecting one of the filter solutions based on the comparison of the computed performance parameters, and constructing the RF filter using the selected filter solution.

A tunable non-reciprocal frequency limiter with an asymmetric micro-electro-mechanical resonator has two independent transducer ports. One port has a film stack including a 10 nm hafnium zirconium oxide (HZO) and another port has a film stack including a 120 nm aluminum nitride (AlN) film. These film stacks are deposited on top of 70 nm single crystal silicon substrate applying CMOS compatible fabrication techniques. The asymmetric transducer architecture with dissimilar electromechanical coupling coefficients force the resonator into mechanical nonlinearity on actuation with transducer having larger coupling. A proof-of-concept electrically-coupled channel filter is demonstrated with two such asymmetric resonators at ˜253 MHz with individual Q.sub.res of ˜870 and a non-reciprocal transmission ratio (NTR) ˜16 dB and BW.sub.3 dB of 0.25%.

A method of manufacturing a ceramic resonator radio frequency filter includes placing one or more first coaxial resonators on a printed circuit board, and placing one or more second coaxial resonators over the one or more first coaxial resonators so that the coaxial resonators are arranged in a stacked configuration on the printed circuit board. The method also includes electrically connecting the one or more first coaxial resonators and second coaxial resonators to the printed circuit board.

A microelectromechanical resonator includes a support structure, a resonator element suspended to the support structure, and an actuator for exciting the resonator element to a resonance mode. The resonator element includes a plurality of adjacent sub-elements each having a length and a width and a length-to-width aspect ratio of higher than 1 and being adapted to a resonate in a length-extensional, torsional or flexural resonance mode. Further, each of the sub-elements is coupled to at least one other sub-element by one or more connection elements coupled to non-nodal points of the of said resonance modes of the sub-elements for exciting the resonator element into a collective resonance mode.

A method for electronic circuit spectral analysis includes receiving a list of parts for an electronic circuit, determining a part admittance matrix with algebraic nodes for each part, and determining a circuit admittance matrix for exterior nodes, interior nodes, and algebraic nodes based on the part admittance matrices. The method also includes reducing interior nodes of the circuit admittance matrix for exterior nodes, interior nodes, and algebraic nodes to determine a circuit admittance matrix for exterior nodes and algebraic nodes, reducing algebraic nodes to transform the circuit admittance matrix for exterior nodes and algebraic nodes into a Green's Function, evaluating the Green's Function to determine a circuit exterior node admittance matrix over a frequency spectrum, and transforming the circuit exterior node admittance matrix to a circuit scattering matrix over the frequency spectrum.

A resonator system is provided in which a combined overtone resonator device is excited with a two-dimensional mode of mechanical vibration in a cross sectional plane of a piezoelectric plate in response to an alternating voltage applied through an interdigitated electrode. The cross sectional plane extends along the width direction and the thickness direction, and the two-dimensional mode of mechanical vibration is a two-dimensional combined overtone mode of second and third order asymmetrical Lamb-wave overtones.

In an embodiment, a tunable stiffness mechanical filter is provided including an input coupler to a negative stiffness structure with a negative stiffness characteristic, and further including a tuner for tuning the negative stiffness structure. An output sensor is located along the negative stiffness structure. The filter may include an amplifier and/or a driver coupled between the output sensor and the negative stiffness structure.

A microelectromechanical resonator includes a support structure, a resonator element suspended to the support structure, and an actuator for exciting the resonator element to a resonance mode. The resonator element includes a plurality of adjacent sub-elements each having a length and a width and a length-to-width aspect ratio of higher than 1 and being adapted to a resonate in a length-extensional, torsional or flexural resonance mode. Further, each of the sub-elements is coupled to at least one other sub-element by one or more connection elements coupled to non-nodal points of the of said resonance modes of the sub-elements for exciting the resonator element into a collective resonance mode.

A microelectromechanical resonator assembly includes a first rectangular resonator array and a second rectangular resonator array, where the first rectangular resonator array and the second rectangular resonator array each have at least two rectangular resonator sub-elements, and the at least two rectangular resonator sub-elements are coupled to each other by one or more connection elements, and the first rectangular resonator array and the second rectangular resonator array are coupled to each other by one or more connection elements.

A combination filter comprises a notch filter formed of acoustic wave resonators and a cavity filter electrically in series with the notch filter to provide for the combination filter to operate at higher powers and frequencies.